The previous lecture in this series is here. The next lecture in this series is here.
We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot “hear the shape of a drum”, and calculate the number of minimal vectors in the Leech lattice, and show that any even unimodular lattice has to have dimension divisible by 8.
This video is part of a lecture course by Richard Borcherds from 2021.